Characterizations of certain Morita context rings

Chimal-Dzul, Henry; López-Permouth, Sergio R.; Szabo, Steve

doi:10.1080/00927872.2021.1897607

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Properties Of the Jacobson Radical Class1

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2021

2023

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Cited by 4 publications

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“…Hence, we start from the definition of a ring of Morita Context. Some studies on ring of Morita context can be seen in [1,11,16] and [12]. Furthermore, the relationship between radical class of rings and the concept of the ring of Morita context starts from the following definition.…”

Section: Properties Of the Jacobson Radical Classmentioning

confidence: 99%

On the restricted graded Jacobson radical of rings of Morita Context

2021

Turk J Math

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The class of rings J = {A|(A, •) forms a group } forms a radical class and it is called the Jacobson radical class. For any ring A , the Jacobson radical J (A) of A is defined as the largest ideal of A which belongs to J . In fact, the Jacobson radical is one of the most important radical classes since it is use widely in another branch of abstract algebra, for example, to construct a two-sided brace. On the other hand, for every ring of Morita context T = R V W S , we will show directly by the structure of the Jacobson radical of rings that the Jacobson radicalwhere J (R) and J (S) are the Jacobson radicals of R and S , respectively, V0 = {v ∈ V |vW ⊆ J (R)} and W0 = {w ∈ W |wV ⊆ J (S)} . This clearly shows that the Jacobson radical is an N − radical. Furthermore, weshow that this property is also valid for the restricted G− graded Jacobson radical of graded ring of Morita context.

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